I understand an ESC must be able to handle full amperage of the motor, and that you can't use an ESC that is half size and just run it at half throttle. Is the nature of Lipo batteries such that one can size the battery for half throttle? Or must their size also be able to handle full amperage? Got a plane I'd like to run at much less than full throttle and would like to use a smaller lighter Lipo but don't understand if the nature of Lipo's allows this?

You can use an ESC with half the rating of the motor as long as you adjust the prop so that it also will use half the power the motor could put out. Everything in balance.